# Full text of "Analytical Mechanics"

## See other formats

```ENERGY                                     195
energy of a body, due to gravitational forces, is a function of the vertical height of the body above the sea level; in fact it equals mgh, where mg is the weight of the body and h its height above the sea level.
162. Difference of Potential Energy. — The difference between the potential energy of a system in two different configurations equals the work done in taking the system from the configuration of lower potential energy to that of higher potential energy.
Let the point A, Fig. 102, represent the standard configuration and the points B and C represent 'two other con-
B
FIG. 102.
figurations.   Then if UB and Uc denote the potential energies at B and C respectively, then by definition
where WAB and WAG are equal, respectively, to the work done in going from A to B and from A to C. Therefore
UC~UB= WAC - WAB = WBC,              (VIII)
where WBC equals the work done in taking the system from B to C. Thus the work done against conservative forces acting upon a system equals the increase in the potential energy of the system.
163. Isolated System. — A system which is not acted upon by external forces is called an isolated system. An isolated system neither gives energy to external bodies nor receives energy from them. This is an immediate result of the definition of an isolated system, because exchange of energy```